How Does Magnetic Flux and Peak EMF Relate in a Solenoid-Coil System?

champ0342
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A coil is located at the center of a long solenoid of radius R = 15cm which has 5x10^7 turns per meter and carries a current I = 16A. The coil is coaxial with the solenoid and consists of 5 turns of wire each in the shape of a square of length a = 5cm on each side.What is the magnetic flux passing through each loop of the coil? If the current in the solenoid is not constan but varies as I=Im cos wt, where I am = 16A and w = 10rad/sec, find the peak emf induced in the coil.



I would like to offer relevant equations but I don't think I have any. I have tried the equations I thought were relevant without coming up with the correct equation



flux = NiA -> 16*.05*5=4 but the correct answer is 2.5. I haven't even got a clue about peak emf...
 
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Magnetic field B at the center of a long solenoid is mu_0*n*I, where mu_0 = 4*pi*10^-7. And flux = B*A
 
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